Which of the following data sets best approximates a standard normal distribution?

• A. A data set with a mean of $\mu =0$ and a standard deviation of $\sigma =1$, with values symmetrically distributed around the mean
• B. A data set with a mean of $\mu =0$ and a standard deviation of $\sigma =1$, but with most values clustered at the extremes
• C. A data set with a mean of $\mu =10$ and a standard deviation of $\sigma =5$, with values skewed to the right
• D. A data set with a mean of $\mu =5$ and a standard deviation of $\sigma =0.5$, with values symmetrically distributed

Answer: (A)

Verified step by step guidance

1. Recall that a standard normal distribution is a special case of the normal distribution with a mean (\mu) of 0 and a standard deviation (\sigma) of 1.
2. Understand that the shape of a normal distribution is symmetric and bell-shaped, meaning values are evenly distributed around the mean without skewness.
3. Evaluate each data set by checking if the mean is 0 and the standard deviation is 1, as these are defining parameters of the standard normal distribution.
4. Check the distribution of values: the data should be symmetrically distributed around the mean, not clustered at extremes or skewed to one side.
5. Conclude that the data set best approximating a standard normal distribution is the one with mean 0, standard deviation 1, and values symmetrically distributed around the mean.